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Evaluate the following limit: lim(nto ...

Evaluate the following limit:
`lim_(nto oo)(sum_(r=1)^(n) sqrt(r)sum_(r=1)^(h)1/(sqrt(r)))/(sum_(r=1)^(n)r)`

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CENGAGE ENGLISH-INTEGRALS-All Questions
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  2. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

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  3. Evaluate the following limit: lim(nto oo)(sum(r=1)^(n) sqrt(r)sum(r=...

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  7. If fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a ...

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  8. If f(x)=min(|x|,1-|x|,1/4)AAx in R , then find the value of int(-1)^1...

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  11. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|+pi/3))dx

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  12. Evaluate: ("lim")(n rarr oo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(s...

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  13. If y(x)=int(pi^2/16)^(x^2)(cosxcossqrt(theta))/(1+sin^2sqrt(theta))d t...

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  14. Evaluate: ("lim")(nvecoo)[1/(n^2)sec^2 1/(n^2)+2//n^2sec^2 4/(n^2)++1/...

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  15. For x >0,l e tf(x)=int1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/...

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  16. Evaluate ("lim")(n rarr oo)sum(k=1)^nk/(n^2+k^2)

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  17. If" f, is a continuous function with int0^x f(t) dt->oo as |x|->ooth...

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  18. Prove that pi/6 lt int0^1(dx) (sqrt(4-x^2-x^3)) lt pi/(4sqrt(2))

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  19. Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)fo...

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  20. Prove that int0^x e^(x t-t^2) dt=e^(x^(2)/4)int0^x e^-(t^(2)/4)dt

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